{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e055c9b530ac4496c965f22a24f19356949d8300f48f1adcdffbfe224a099a31","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["3effcf478c7155a478a70f525bdf9d68613645a3c457ace60b345c39d6e152c1","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"2649a9da72da8ae558cf11323fbe8655737010431cf6919bef98008896614601","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"cm.chaos-scrambling.bound-saturation","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Theory says scrambling at temperature $T$ cannot grow faster than the rate $2\\pi k_{\\mathrm{B}} T/\\hbar$, and black holes and SYK reach this limit. Whether any laboratory material or ordinary lattice model in which each site holds only a few quantum states reaches it is unknown.","posed_since":"2015","precise":"The Maldacena-Shenker-Stanford bound $\\lambda_L \\le 2\\pi k_B T/\\hbar$ holds for regularized thermal OTOCs, and large-N lattice models (SYK chains, Gu, Qi, Stanford 2017) saturate it. For a lattice model with fixed, finite local Hilbert-space dimension (no large-N or semiclassical parameter), determine whether a parametrically wide exponential-growth window exists as $T \\to 0$ and, if so, whether $\\lambda_L \\hbar/(2\\pi k_B T) \\to 1$ can be reached; or prove a bound strictly below 1. Answer: an explicit model or a bound.","problem_ref":"3effcf478c7155a478a70f525bdf9d68613645a3c457ace60b345c39d6e152c1","references":"","settled_by":"A controlled computation of $\\lambda_{\\mathrm{L}}(T)$ in a microscopic lattice model with finite local dimension, or direct OTOC measurement in a quantum simulator at temperatures where quantum effects dominate.","status_note":"Large-N lattice models saturate the bound; no finite-local-dimension example is known.","title":"Can a lattice with few states per site saturate the chaos bound?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5a02d079e97059750b8620f809dded99b9ba5bfef93b5bb9b3d72ecffbce8084","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7036e80836d49cd3badb62f4bc7c399feb7e5b50c4749d8c35e8d4d07f50f5b0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"GCCY7YE7THnBUX6Vtn-JwZXWWz71cdIgtaqAOLPYEyJFEUy11KCTcrOqpZKnDUQb1b3G1Zp75iSVBzFyfrYVDA"},"schema":"pubphys.envelope/1"},"record_hash":"5a02d079e97059750b8620f809dded99b9ba5bfef93b5bb9b3d72ecffbce8084","leaf_index":2702}